In non-negative matrix factorization, it is difficult to find the optimal non-negative factor matrix in each iterative update. However, with the help of transformation matrix, it is able to derive the optimal non-negative factor matrix for the transformed cost function. Transformation matrix based nonnegative matrix factorization method is proposed and analyzed. It shows that this new method, w...

General thermo-mechanical behavior of composites reinforced by shape memory alloy fibers is predicted using a three-dimensional analytical micromechanical method to consider the effect of fibers activation. Composite due to the micromechanical method can be exposed to general normal and shear mechanical and thermal loading which cause to activate the shape memory alloy fibers within polymeric m...

This paper presents a new iterative algorithm as an upgrade to sufficient LMI conditions for the H∞ static-output-feedback (SOF) control of discrete-time systems. Based on an analysis of the structures of the coordinate transformation matrix and the Lyapunov matrix, the open question of how to fix the Lyapunov matrix structure raised by G. I. Bara and M. Boutayeb is replaced with the question o...

Abstract—Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables...

Transformation theory is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by selection of the matrix relating displacements in the two descriptions. This gauge matrix can be chosen to make the transformed density isotropic for any transformation although the stress i...

The covariance matrix of a pattern is composed by its second order central moments. For a rotationally symmetric shape, its covariance matrix is a scalar identity matrix. In this work, we apply this property to restore the skewed shape of rotational symmetry. The relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived. By computing ...

incorporation of copper species into silica matrix was performed by the sol-gel method. copper ions and copper particles were doped using two different copper sources; cu(no3)2.3h2o and copper particles chemically synthesized.the particles of copper metallic, cuprous and cupric oxide were prepared and the synthesis and characterizations of copper species were compared together. on the other han...

In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini’s type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation ...

This paper is concerned with accurate computations for matrix multiplication. An error-free transformation of matrix multiplication is developed by the authors. It transforms a product of two floatingpoint matrices to a sum of several floating-point matrices by using only floating-point arithmetic. This transformation is useful not only for accurate matrix multiplication but also for interval e...

In 1853 Hamilton showed that a general linear vector transformation in three dimensions satisfied a third-order equation. In this paper we indicate how Hamilton came to consider this transformation and what he did with it. Hamilton’s work was written in the language of quaternions, which he invented. We describe this work using vectors instead of the quaternions. In addition, we express Hamilto...